The Additive Problem for the Number of Representations as a Sum of Two Squares

We improve a previous unconditional result about the asymptotic behavior of ∑ n ≤ x r ( n ) r ( n + m ) with r ( n ) the number of representations of n as a sum of two squares when m may vary with x .

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 44
Main Author: Chamizo, Fernando
Format: Article
Language:English
Subjects:
Asymptotic properties
Mathematics
Mathematics and Statistics
Representations
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Description
Summary:We improve a previous unconditional result about the asymptotic behavior of ∑ n ≤ x r ( n ) r ( n + m ) with r ( n ) the number of representations of n as a sum of two squares when m may vary with x .
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01959-3